Metal Colanders can be washed in the dishwasher.
But if you have an enameled Colander then it should not be put in the dishwasher because enameled Colanders can chip in the dishwasher as it can get banged around in the dishwasher against the dishwasher racks.
Metal Colanders are okay to put in the dishwasher but just be aware that the metal Colander may cause chipping of the paint on your dishwasher rack which could lead to the dishwasher rack rusting in some spots.
However its not gonna harm the dishwasher much or harm the Colander to wash it in the dishwasher.
I always have washed my metal Colander in the dishwasher and it has never been an issue for me.
Most of my dishes do get washed in the dishwasher as I hate washing dishes by hand.
The dishwasher does most of the work at cleaning my dishes including my metal Colander.